MinT - Information on Result #896373

Information on Result #896373

Linear OOA(7⁶⁶, 8427, F₇, 2, 13) (dual of [(8427, 2), 16788, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7¹⁰, 21, F₇, 2, 6) (dual of [(21, 2), 32, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(7³, 8, F₇, 2, 3) (dual of [(8, 2), 13, 4]-NRT-code), using
    - extended Reedâ€“Solomon NRT-code RS_e(2;13,7) [i]
  2. linear OOA(7⁷, 13, F₇, 2, 6) (dual of [(13, 2), 19, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (1, 7, 13)-net over F₇, using
      - 6 times m-reduction [i] based on digital (1, 13, 13)-net over F₇, using
        a shift-net [i]
linear OOA(7⁵⁶, 8406, F₇, 2, 13) (dual of [(8406, 2), 16756, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(7⁵⁶, 16812, F₇, 13) (dual of [16812, 16756, 14]-code), using
  - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
    1. linear OA(7⁵⁶, 16807, F₇, 13) (dual of [16807, 16751, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
    2. linear OA(7⁵¹, 16807, F₇, 12) (dual of [16807, 16756, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
    3. linear OA(7⁰, 5, F₇, 0) (dual of [5, 5, 1]-code), using
      - discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.